%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP055-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:10 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.47s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP055-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:17:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.47 Command-line arguments: --no-flatten-goal
% 0.09/0.47
% 0.09/0.47 % SZS status Unsatisfiable
% 0.09/0.47
% 0.62/0.53 % SZS output start Proof
% 0.62/0.53 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))) = Y.
% 0.62/0.53
% 0.62/0.53 Lemma 2: multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))) = inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X))).
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))), multiply(inverse(X), inverse(multiply(inverse(X), X))))))), multiply(Z, X)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, X)))
% 0.62/0.53
% 0.62/0.53 Lemma 3: multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z)) = Y.
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), multiply(inverse(V), inverse(multiply(inverse(V), V))))))), multiply(W, V)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 Y
% 0.62/0.53
% 0.62/0.53 Lemma 4: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(W, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(U), inverse(multiply(inverse(U), U))))))), multiply(V, U)))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.62/0.53
% 0.62/0.53 Lemma 5: multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W)) = multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W)).
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(X, multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))
% 0.62/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.53 multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), multiply(inverse(multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), W))
% 0.62/0.53 = { by lemma 4 R->L }
% 0.62/0.53 multiply(inverse(multiply(V, multiply(Y, Z))), multiply(V, W))
% 0.62/0.53
% 0.62/0.53 Lemma 6: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(inverse(Y), Y)
% 0.62/0.53 = { by lemma 3 R->L }
% 0.62/0.53 multiply(inverse(Y), multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(Y)), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(Z, W)))
% 0.62/0.53 = { by lemma 5 }
% 0.62/0.53 multiply(inverse(multiply(V, multiply(Z, W))), multiply(V, multiply(Z, W)))
% 0.62/0.53 = { by lemma 5 R->L }
% 0.62/0.53 multiply(inverse(X), multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(X)), multiply(inverse(W), inverse(multiply(inverse(W), W))))))), multiply(Z, W)))
% 0.62/0.53 = { by lemma 3 }
% 0.62/0.53 multiply(inverse(X), X)
% 0.62/0.53
% 0.62/0.53 Lemma 7: inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))) = multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(W), W)))).
% 0.62/0.53 Proof:
% 0.62/0.53 inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))
% 0.62/0.53 = { by lemma 2 R->L }
% 0.62/0.53 multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))
% 0.62/0.53 = { by lemma 6 R->L }
% 0.62/0.53 multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))
% 0.62/0.53 = { by lemma 6 R->L }
% 0.62/0.53 multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(W), W))))
% 0.62/0.53
% 0.62/0.53 Lemma 8: multiply(inverse(X), inverse(multiply(inverse(X), multiply(inverse(Y), Y)))) = inverse(multiply(inverse(Z), Z)).
% 0.62/0.53 Proof:
% 0.62/0.53 multiply(inverse(X), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))
% 0.62/0.53 = { by lemma 7 R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(W, X)), multiply(W, X)))
% 0.62/0.53 = { by lemma 6 R->L }
% 0.62/0.53 inverse(multiply(inverse(Z), Z))
% 0.62/0.53
% 0.62/0.53 Lemma 9: inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.62/0.53 Proof:
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.62/0.53 = { by lemma 2 R->L }
% 0.62/0.53 inverse(multiply(inverse(multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z))))))))), multiply(inverse(Z), inverse(multiply(inverse(Z), Z)))))
% 0.62/0.53 = { by axiom 1 (single_axiom) }
% 0.62/0.53 Y
% 0.62/0.53
% 0.62/0.53 Lemma 10: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z))))) = Y.
% 0.62/0.53 Proof:
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))
% 0.62/0.53 = { by lemma 6 }
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.62/0.53 = { by lemma 6 }
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))
% 0.62/0.53 = { by lemma 9 }
% 0.62/0.53 Y
% 0.62/0.53
% 0.62/0.53 Lemma 11: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.62/0.53 Proof:
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(Y), Y)))
% 0.62/0.53 = { by lemma 6 }
% 0.62/0.53 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), multiply(inverse(inverse(multiply(inverse(Z), Z))), inverse(multiply(inverse(Z), Z)))))
% 0.62/0.53 = { by lemma 10 }
% 0.62/0.54 inverse(multiply(inverse(Z), Z))
% 0.62/0.54
% 0.62/0.54 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.62/0.54 Proof:
% 0.62/0.54 inverse(multiply(inverse(X), X))
% 0.62/0.54 = { by lemma 8 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), multiply(inverse(Z), Z))), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), multiply(inverse(Z), Z))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.62/0.54 = { by lemma 11 }
% 0.62/0.54 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), multiply(inverse(Z), Z))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))))
% 0.62/0.54 = { by lemma 7 }
% 0.62/0.54 multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z)))))
% 0.62/0.54 = { by lemma 6 R->L }
% 0.62/0.54 multiply(inverse(Y), Y)
% 0.62/0.54
% 0.62/0.54 Lemma 13: inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z)))) = Y.
% 0.62/0.54 Proof:
% 0.62/0.54 inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), inverse(multiply(inverse(V), V)))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(Y), inverse(multiply(inverse(V), V)))))
% 0.62/0.54 = { by lemma 10 }
% 0.62/0.54 Y
% 0.62/0.54
% 0.62/0.54 Lemma 14: inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), Z))) = multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(W), W)))).
% 0.62/0.54 Proof:
% 0.62/0.54 inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), Z)))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z)))
% 0.62/0.54 = { by lemma 7 }
% 0.62/0.54 multiply(inverse(Z), inverse(multiply(inverse(Y), multiply(inverse(W), W))))
% 0.62/0.54
% 0.62/0.54 Lemma 15: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(Z), Z)))) = Y.
% 0.62/0.54 Proof:
% 0.62/0.54 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.62/0.54 = { by lemma 14 R->L }
% 0.62/0.54 inverse(multiply(multiply(inverse(V), V), multiply(inverse(Y), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 13 }
% 0.62/0.54 Y
% 0.62/0.54
% 0.62/0.54 Lemma 16: multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z))) = Y.
% 0.62/0.54 Proof:
% 0.62/0.54 multiply(multiply(inverse(X), X), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z)))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(inverse(Y)), multiply(inverse(Z), Z)))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(inverse(Y)), inverse(multiply(inverse(V), V))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(inverse(Y)), inverse(multiply(inverse(V), V))))
% 0.62/0.54 = { by lemma 13 R->L }
% 0.62/0.54 inverse(multiply(multiply(inverse(T), T), multiply(inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(inverse(Y)), inverse(multiply(inverse(V), V))))), multiply(inverse(S), S))))
% 0.62/0.54 = { by lemma 10 }
% 0.62/0.54 inverse(multiply(multiply(inverse(T), T), multiply(inverse(Y), multiply(inverse(S), S))))
% 0.62/0.54 = { by lemma 13 }
% 0.62/0.54 Y
% 0.62/0.54
% 0.62/0.54 Lemma 17: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(multiply(inverse(W), W), multiply(inverse(Y), Z)).
% 0.62/0.54 Proof:
% 0.62/0.54 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.62/0.54 = { by lemma 4 }
% 0.62/0.54 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 0.62/0.54 = { by lemma 6 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), Z))
% 0.62/0.54 = { by lemma 12 }
% 0.62/0.54 multiply(multiply(inverse(W), W), multiply(inverse(Y), Z))
% 0.62/0.54
% 0.62/0.54 Lemma 18: inverse(multiply(multiply(inverse(X), X), multiply(Y, Z))) = multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(W), W))).
% 0.62/0.54 Proof:
% 0.62/0.54 inverse(multiply(multiply(inverse(X), X), multiply(Y, Z)))
% 0.62/0.54 = { by lemma 9 R->L }
% 0.62/0.54 inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, Y)), multiply(V, U)))), multiply(inverse(U), inverse(multiply(inverse(U), U))))), Z)))
% 0.62/0.54 = { by lemma 14 }
% 0.62/0.54 multiply(inverse(Z), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(V, Y)), multiply(V, U)))), multiply(inverse(U), inverse(multiply(inverse(U), U))))), multiply(inverse(inverse(multiply(inverse(multiply(V, Y)), multiply(V, U)))), inverse(multiply(inverse(multiply(V, Y)), multiply(V, U)))))))
% 0.62/0.54 = { by lemma 7 }
% 0.62/0.54 multiply(inverse(Z), multiply(inverse(inverse(multiply(inverse(multiply(V, Y)), multiply(V, U)))), inverse(multiply(inverse(multiply(inverse(U), inverse(multiply(inverse(U), U)))), multiply(inverse(U), U)))))
% 0.62/0.54 = { by lemma 7 }
% 0.62/0.54 multiply(inverse(Z), multiply(inverse(multiply(inverse(U), inverse(multiply(inverse(Y), multiply(inverse(W), W))))), inverse(multiply(inverse(multiply(inverse(U), inverse(multiply(inverse(U), U)))), multiply(inverse(U), U)))))
% 0.62/0.54 = { by lemma 7 }
% 0.62/0.54 multiply(inverse(Z), multiply(inverse(multiply(inverse(U), inverse(multiply(inverse(Y), multiply(inverse(W), W))))), multiply(inverse(U), inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(T), T))))))
% 0.62/0.54 = { by lemma 17 }
% 0.62/0.54 multiply(inverse(Z), multiply(multiply(inverse(S), S), multiply(inverse(inverse(multiply(inverse(Y), multiply(inverse(W), W)))), inverse(multiply(inverse(inverse(multiply(inverse(U), U))), multiply(inverse(T), T))))))
% 0.62/0.54 = { by lemma 11 }
% 0.62/0.54 multiply(inverse(Z), multiply(multiply(inverse(S), S), multiply(inverse(inverse(multiply(inverse(Y), multiply(inverse(W), W)))), inverse(multiply(inverse(X2), X2)))))
% 0.62/0.54 = { by lemma 12 }
% 0.62/0.54 multiply(inverse(Z), multiply(multiply(inverse(S), S), multiply(inverse(inverse(multiply(inverse(Y), multiply(inverse(W), W)))), multiply(inverse(Y2), Y2))))
% 0.62/0.54 = { by lemma 16 }
% 0.62/0.54 multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(W), W)))
% 0.62/0.54
% 0.62/0.54 Lemma 19: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 0.62/0.54 Proof:
% 0.62/0.54 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 0.62/0.54 = { by lemma 15 R->L }
% 0.62/0.54 multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 7 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(U), U))), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(U), U))), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(S), S), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 16 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(multiply(inverse(X2), X2), multiply(inverse(inverse(multiply(inverse(S), S))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(multiply(inverse(S), S))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 12 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), inverse(multiply(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(U2), inverse(multiply(inverse(U2), U2))))))), multiply(V2, U2))))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 11 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), inverse(multiply(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))), multiply(inverse(U2), inverse(multiply(inverse(U2), U2))))))), multiply(V2, U2))))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by axiom 1 (single_axiom) }
% 0.62/0.54 multiply(inverse(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 7 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(T2), T2))), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))), multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(T2), T2))), inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))))
% 0.62/0.54 = { by lemma 18 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))), multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(T2), T2))), inverse(multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(Y2), Y2))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))))
% 0.62/0.54 = { by lemma 18 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))), multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(T2), T2))), inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))))
% 0.62/0.54 = { by lemma 7 R->L }
% 0.62/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(S2, X)), multiply(S2, multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))), multiply(multiply(inverse(multiply(inverse(Z2), Z2)), multiply(inverse(inverse(inverse(multiply(inverse(W2), W2)))), multiply(inverse(T2), T2))), inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))))
% 0.62/0.54 = { by lemma 18 R->L }
% 0.62/0.54 inverse(multiply(inverse(inverse(multiply(inverse(multiply(S2, X)), multiply(S2, multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), inverse(multiply(inverse(multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2)))), multiply(multiply(inverse(T), T), multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(Z2), Z2))))))))
% 0.62/0.54 = { by lemma 9 }
% 0.62/0.54 X
% 0.62/0.54
% 0.62/0.54 Lemma 20: multiply(multiply(inverse(X), X), Y) = Y.
% 0.62/0.54 Proof:
% 0.62/0.54 multiply(multiply(inverse(X), X), Y)
% 0.62/0.54 = { by lemma 19 R->L }
% 0.62/0.54 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(Z), Z))))
% 0.62/0.54 = { by lemma 15 }
% 0.62/0.54 Y
% 0.62/0.54
% 0.62/0.54 Lemma 21: multiply(inverse(inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y))))), Z) = Z.
% 0.62/0.54 Proof:
% 0.62/0.54 multiply(inverse(inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y))))), Z)
% 0.62/0.54 = { by lemma 19 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y))))), inverse(multiply(inverse(Z), multiply(inverse(W), W))))
% 0.62/0.54 = { by lemma 19 R->L }
% 0.62/0.54 multiply(inverse(inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y))))), inverse(multiply(inverse(inverse(multiply(inverse(Z), multiply(inverse(W), W)))), multiply(inverse(V), V))))
% 0.62/0.54 = { by lemma 7 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Z), multiply(inverse(W), W))))), multiply(X, inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y)))))))
% 0.62/0.54 = { by lemma 19 R->L }
% 0.62/0.54 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), inverse(multiply(inverse(Z), multiply(inverse(W), W))))), multiply(X, inverse(multiply(X, multiply(inverse(X), multiply(inverse(Y), Y)))))))
% 0.62/0.55 = { by lemma 19 R->L }
% 0.62/0.55 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), inverse(multiply(inverse(Z), multiply(inverse(W), W))))), multiply(X, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y)))))))
% 0.62/0.55 = { by lemma 7 R->L }
% 0.62/0.55 inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(X), multiply(inverse(Y), Y)))))), multiply(X, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y)))))))
% 0.62/0.55 = { by lemma 19 R->L }
% 0.62/0.55 inverse(multiply(inverse(inverse(multiply(inverse(multiply(U, Z)), multiply(U, multiply(inverse(X), multiply(inverse(Y), Y)))))), multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), multiply(inverse(Y), Y)))))))
% 0.62/0.55 = { by lemma 9 }
% 0.62/0.55 Z
% 0.62/0.55
% 0.62/0.55 Lemma 22: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 0.62/0.55 Proof:
% 0.62/0.55 inverse(multiply(inverse(X), Y))
% 0.62/0.55 = { by lemma 21 R->L }
% 0.62/0.55 inverse(multiply(inverse(X), multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), multiply(inverse(W), W))))), Y)))
% 0.62/0.55 = { by lemma 21 R->L }
% 0.62/0.55 inverse(multiply(inverse(multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), multiply(inverse(W), W))))), X)), multiply(inverse(inverse(multiply(Z, multiply(inverse(Z), multiply(inverse(W), W))))), Y)))
% 0.62/0.55 = { by lemma 7 }
% 0.62/0.55 multiply(inverse(Y), inverse(multiply(inverse(X), multiply(inverse(V), V))))
% 0.62/0.55 = { by lemma 19 }
% 0.62/0.55 multiply(inverse(Y), X)
% 0.62/0.55
% 0.62/0.55 Lemma 23: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.62/0.55 Proof:
% 0.62/0.55 multiply(inverse(X), X)
% 0.62/0.55 = { by lemma 12 R->L }
% 0.62/0.55 inverse(multiply(inverse(Z), Z))
% 0.62/0.55 = { by lemma 8 R->L }
% 0.62/0.55 multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Y), multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Y), multiply(inverse(V), V)))), multiply(inverse(Y), Y))))
% 0.62/0.55 = { by lemma 13 }
% 0.62/0.55 multiply(Y, inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Y), multiply(inverse(V), V)))), multiply(inverse(Y), Y))))
% 0.62/0.55 = { by lemma 13 }
% 0.62/0.55 multiply(Y, inverse(multiply(Y, multiply(inverse(Y), Y))))
% 0.62/0.55 = { by lemma 19 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(Y, multiply(inverse(Y), inverse(multiply(inverse(Y), multiply(inverse(U), U)))))))
% 0.62/0.55 = { by lemma 7 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(Y, inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y))))))
% 0.62/0.55 = { by lemma 20 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(multiply(multiply(inverse(Y), Y), Y), inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y))))))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(Y), Y)), Y), inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y))))))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(multiply(inverse(inverse(multiply(inverse(Y), Y))), Y), inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y))))))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 multiply(Y, inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))), inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y))))))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 multiply(Y, inverse(inverse(multiply(inverse(inverse(multiply(inverse(multiply(T, Y)), multiply(T, Y)))), multiply(inverse(Y), inverse(multiply(inverse(Y), Y)))))))
% 0.62/0.55 = { by lemma 9 }
% 0.62/0.55 multiply(Y, inverse(Y))
% 0.62/0.55
% 0.62/0.55 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.62/0.55 Proof:
% 0.62/0.55 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.62/0.55 = { by lemma 20 }
% 0.62/0.55 tuple(multiply(inverse(a1), a1), a2, multiply(multiply(a3, b3), c3))
% 0.62/0.55 = { by lemma 23 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 0.62/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, multiply(multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), b3), c3))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z)))), c3))
% 0.62/0.55 = { by lemma 22 R->L }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(c3), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by axiom 1 (single_axiom) R->L }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(W, b3)))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 22 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(multiply(W, b3)), multiply(W, inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 17 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(multiply(inverse(V), V), multiply(inverse(b3), inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))))))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 20 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), inverse(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(b3), b3))))))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 22 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), multiply(inverse(multiply(inverse(b3), inverse(multiply(inverse(b3), b3)))), c3))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 22 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), multiply(multiply(inverse(inverse(multiply(inverse(b3), b3))), b3), c3))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 22 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), multiply(multiply(inverse(multiply(inverse(b3), b3)), b3), c3))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.55 = { by lemma 22 }
% 0.62/0.55 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), multiply(multiply(multiply(inverse(b3), b3), b3), c3))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.56 = { by lemma 20 }
% 0.62/0.56 tuple(multiply(X, inverse(X)), a2, inverse(multiply(inverse(multiply(inverse(b3), multiply(b3, c3))), multiply(inverse(b3), multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))))))
% 0.62/0.56 = { by lemma 7 }
% 0.62/0.56 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), inverse(multiply(inverse(multiply(b3, c3)), multiply(inverse(U), U)))))
% 0.62/0.56 = { by lemma 19 }
% 0.62/0.56 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(Y, inverse(multiply(inverse(a3), multiply(inverse(Z), inverse(multiply(inverse(Z), Z))))))), multiply(Y, Z))), multiply(b3, c3)))
% 0.62/0.56 = { by axiom 1 (single_axiom) }
% 0.62/0.56 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 0.62/0.56 = { by lemma 23 R->L }
% 0.62/0.56 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.62/0.56 % SZS output end Proof
% 0.62/0.56
% 0.62/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------